I would like to roll some OSS in the public domain into a larger code base to distribute myself. I have a few concerns however.

Code released into the public domain may at the discretion of the author be placed under any other more restrictive license.

Public domain is not cleanly recognized across jurisdictions (e.g. in the EU I understand that it gets a little bit messy)

So my thinking is this: I live in the U.S. - Even though I did not write the software myself, can I re-license it as CC0, effectively keeping it in the public domain while still declaring a more effective 'license'?

Edit (2017-06-12): I'm getting some downvotes on this question, and I think the reason is that some of the nuance to which I'm asking is unclear.

In this case the origin of the code does not matter. What matters is how the jurisdiction in which it will be distributed interprets the license. (Please correct me if I am wrong!)

In the answer linked by @unor, there does not seem to be a clear consensus about what ultimately applies. The most upvoted answer concludes that no one can stop someone from re-licensing, but what no one addresses is whether or not the new license will hold any water.

Thanks for the help all, I'm still convinced that I have a unique question so if you think that there is a problem, please help me reconcile it!

You do not provide sufficient information on the origin of public domain code. How did it came into the public domain. Was it declared as such by the developer? In which terms? Was it developed by a US federal employee?
– Zimm i48May 11 '17 at 10:20